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Modules invariant under automorphisms of their covers and envelopes

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Abstract

In this paper we develop a general theory of modules which are invariant under automorphisms of their covers and envelopes. When applied to specific cases like injective envelopes, pure-injective envelopes, cotorsion envelopes, projective covers, or flat covers, these results extend and provide a much more succinct and clear proofs for various results existing in the literature. Our results are based on several key observations on the additive unit structure of von Neumann regular rings.

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Authors and Affiliations

  1. Departamento de Mathematicas, Universidad de Murcia, Murcia, 30100, Spain

    Pedro A. Guil Asensio

  2. Department of Mathematics, Hacettepe University, Ankara, 06800, Turkey

    Derya Keskin Tütüncü

  3. Department of Mathematics and Computer Science, St. Louis University, St. Louis, MO, 63103, USA

    Ashish K. Srivastava

Authors
  1. Pedro A. Guil Asensio
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  2. Derya Keskin Tütüncü
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  3. Ashish K. Srivastava
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Corresponding author

Correspondence to Pedro A. Guil Asensio.

Additional information

The first author was partially supported by the DGI (MTM2010-20940-C02-02) and by the Excellence Research Groups Program of the Séneca Foundation of the Region of Murcia. Part of the sources of both institutions come from the FEDER funds of the European Union.

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Asensio, P.A.G., Tütüncü, D.K. & Srivastava, A.K. Modules invariant under automorphisms of their covers and envelopes. Isr. J. Math. 206, 457–482 (2015). https://doi.org/10.1007/s11856-014-1147-3

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  • DOI: https://doi.org/10.1007/s11856-014-1147-3

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